Question

A cone of diameter 42 cm has volume 12935 cm cube , find its dlqnt height and curved surface area

Answer 1

Q: A cone of diameter 42 cm has volume 12935 cm^3 , find its slant height and curved surface area.

diameter of cone = 42 cm

Find the radius:
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radius of cone = 42 ÷ 2 = 21 cm

since, we know volume of cone

= πr^2h / 3

Find the height:
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given, volume of cone = 12935 cm^3

πr^2h / 3 = 12935

πr^2h = 12935 × 3

(22/ 7 ) × (21)^2 × h = 12935 × 3

h = ( 12935 × 3 × 7 )/ ( 22 × 21 × 21 )

h = 12935 ÷ ( 22 × 21 )

h = 12935 ÷ 462 = 27.99 = 28 cm

height of the cone = 28 cm

Find the slant height:

slant height l = √[ (r)^2 + ( h)^2 ]

l = √[ (21 )^2 + ( 28 )^2 ]

l = √( 441 + 784) = √1225 = 35 cm

slant height of cone l = 35 cm

Find the CSA:
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curved surface area of cone = πrl

= (22/ 7 ) × ( 21 ) × 35

= 22 × 3 × 35 = 2310 cm^2

Answer:
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(1) slant height of the cone = 35cm

(2)curved surface of cone =2310cm^2